The win put Man. City within three points of United.
Sergio Aguero and Javi Garcia both scored in the first half for the defending champions, before Senegalese Demba Ba score one for the host, in an earlier game played on Saturday.
The Ivorian, Yaya Toure, put it past beyond Newcastle when he scored City’s third goal in the 78th minute.
City will hope that Sunderland defeat Manchester United later on Saturday for them to remain within three points of their city rivals.